OK, letâs start to talk about what these graphs are showing us, and what they can tell us about setting up our systems.
First itâs useful to remember that digital filtering is a balancing act between minimizing frequency-based distortion (aliasing and imaging, where frequencies above the audio band are made by the filter to âfold downâ into the audible frequency range, causing distortion) and minimizing time-based distortion (ringing, more properly the Gibbs effect, where the filter causes oscillation at the frequency where it cuts the signal).
Regarding aliasing, letâs look at the first two images showing the transition bands for r8brain 1.5 linear phase and SoX 14.4 intermediate phase. Both filters do very nicely, beginning to cut above audible frequencies so we donât lose any of the highs, and cutting nearly all response by the Nyquist frequency, 22050Hz, so we wonât have any appreciable aliasing or imaging.
Now letâs look at the impulse responses of these two filters, where we get a somewhat more interesting comparison.
We see with the r8brain linear phase filter there is some pre-ringing, that is, oscillation before the main impulse. A couple of things about this: First, recall that the ringing frequency is at the point where the filter cuts, and we saw this was above audible frequencies. Second, notice the very low amplitude (energy) of the ringing. Given these two facts, it is at least controversial and perhaps even doubtful whether the ringing has any audible effect. This is really saying no more than that the filter, with its cutoff that is not as sharp as the SoX one, is pretty nicely designed to minimize both ringing energy and aliasing/imaging. Finally, one last item of note for the sharp-eyed: The amplitude of the main impulse is quite high, reaching approximately -0.7dB. This means we will hear powerful transients if they are in the musical signal.
Looking at the SoX intermediate phase impulse response, we see unsurprisingly, because phase is timing, that the intermediate phase filter has moved the pre-ringing energy and some of the main impulse energy so it occurs after the main impulse. While there is no pre-ringing, the amplitude of the main impulse is approximately -4.4dB, about 3.7dB down from the r8brain amplitude, quite possibly enough to be audible. And the first few cycles of post-ringing are pretty energetic, though remember again that these are occurring at higher than audible frequency. Thus from the SoX filter, if we hear a difference from the r8brain filter at all, it might be in the form of a less energetic transient response, with a possibility of an enhanced âreverb tailâ to the signal caused by the greater post-ringing energy.
Comparison of r8brain minimum phase and SoX intermediate phase shows the same transition band performance (since we havenât changed that aspect of these filters). Regarding impulse response, we see as we get to minimum phase, there is even lower amplitude of the main impulse and an even longer âreverb tailâ (again emphasizing the ringing is taking place above audible frequencies) than intermediate phase.
Comparing the two linear phase filters, we see the Sox filterâs sharper cutoff results in just very slightly more ringing energy than r8brain, but still quite low, which is to be expected.
Finally, letâs look at the âaliasing enabledâ SoX filter in comparison to r8brain 2.12 linear phase. Note that the SoX filter really minimizes ringing energy in the impulse measurement. But the very gentle cutoff that enables this comes with two costs: The cut starts at the top of the audible range, with thus a very slight possibility of removing a bit of the high end (though unlikely for anyone except very young people); and more importantly, as it says in the filter name, there will be some aliasing with this filter, because it only cuts by 18dB at the Nyquist frequency.
What does all this mean for filter settings in Audirvana?
First, bandwidth: Donât go below 91 (20/22.05), or youâll begin to cut in the audible range. Also remember that ringing occurs at the point of the cutoff, so you may want to put this a bit above the audible range.
Second, attenuation or anti-aliasing: Itâs OK to back off just a little from the maximum on this to minimize ringing energy, but not so much that youâll introduce aliasing/imaging.
Phase: If youâre tremendously worried about pre-ringing, back off to intermediate phase or set to minimum phase, depending on whether youâre using SoX or r8brain. My own personal thinking, and what I think these graphs help to illustrate, is that very low ringing energy above audible frequencies may well not be a problem, and intermediate or minimum phase settings may even cause a loss of energy on transients. But youâre the one listening to your system, so do what sounds best to you.
Finally, filter length (SoX): A longer filter means the filter operates on the signal for a longer time, causing a sharper cutoff and more ringing, so donât make the filter much if any longer than the default.